What usually causes bad warm starting (on
any petrol-fuelled car, not just an Impreza) is what's known as vapour-locking. Basically, the fuel in the lines on top of the engine evaporates from the heat, so there's none there to prime the injectors (or carb) when you go to start it back up. You won't notice anything with the engine running, because the pump's continuously replacing any lost fuel then. With the Impreza's engine layout and the fuel lines all running literally right across the top of the block, the potential for this might well be a bit worse than on a conventional in-line 4-cylinder, admittely.
The only way I could think changing a water temp sensor might help is by keeping engine temp slightly lower, if the old sensor was misreading (less heat = less evaporation), but I doubt very much this is the main problem. The root cause is still going to be either a weak fuel-pump, and/or something in the manifold end of the fuel delivery circuit (fuel lines, fittings, gaskets, o-rings, etc getting marginally porous from age, or a weak FPR), all of which would be totally consistent with the smell of fuel you mentionned.
Of course, if you're going to work your way through figuring out exactly which of those components is to blame, this might be the perfect time to upgrade to a Walbro and/or do a parallel fuel line mod while you're at it
